Simplify the following expression: $ a = \dfrac{-4}{5y - 5} + \dfrac{9}{2} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-4}{5y - 5} \times \dfrac{2}{2} = \dfrac{-8}{10y - 10} $ Multiply the second expression by $\dfrac{5y - 5}{5y - 5}$ $ \dfrac{9}{2} \times \dfrac{5y - 5}{5y - 5} = \dfrac{45y - 45}{10y - 10} $ Therefore $ a = \dfrac{-8}{10y - 10} + \dfrac{45y - 45}{10y - 10} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-8 + 45y - 45}{10y - 10} $ $a = \dfrac{45y - 53}{10y - 10}$